On tilting modules over cluster-tilted algebras

On tilting modules over cluster-tilted algebras

David Smith

Source: Illinois J. Math. Volume 52, Number 4 (2008), 1223-1247.

Abstract

In this paper, we show that the tilting modules over a cluster-tilted algebra A lift to tilting objects in the associated cluster category $\mathcal{C}_{H}$ . As a first application, we describe the induced exchange relation for tilting A-modules arising from the exchange relation for tilting object in $\mathcal{C}_{H}$ . As a second application, we exhibit tilting A-modules having cluster-tilted endomorphism algebras.

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Primary Subjects: 16G20, 18E30

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ijm/1258554359
Zentralblatt MATH identifier: 05660655
Mathematical Reviews number (MathSciNet): MR2595764

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